scholarly journals Complete monotonicity properties for a ratio of gamma functions

2005 ◽  
pp. 26-28 ◽  
Author(s):  
Chao-Ping Chen
Keyword(s):  
Complete Monotonicity ◽  
Gamma Functions ◽  
Monotonicity Properties

scholarly journals Logarithmically complete monotonicity and Shur-convexity for some ratios of gamma functions

2006 ◽  
pp. 88-92 ◽  
Author(s):  
Li Ai-Jun ◽  
Zhao Wei-Zhen ◽  
Chen Chao-Ping
Keyword(s):  
Complete Monotonicity ◽  
Gamma Functions ◽  
Monotonicity Properties ◽  
Schur Convex

Define F(x) = ?(mx) xm-1?m(x) and G(x)- ?(mx) ?m(x). for x > 0 and m = 2 3,?. In this paper, we consider the logarithmically complete monotonicity properties for the function F and 1/G, and we prove that the function ?(x) = ? n i=1 ?(mxi + 1) ?m (x1 + 1) is strictly Schur-convex (-1/m,+?)n.

Some complete monotonicity properties for the -gamma function

2013 ◽  
Vol 219 (21) ◽  
pp. 10538-10547 ◽  
Author(s):  
V.B. Krasniqi ◽  
H.M. Srivastava ◽  
S.S. Dragomir
Keyword(s):  
Gamma Function ◽  
Complete Monotonicity ◽  
Monotonicity Properties

scholarly journals On the complete monotonicity of quotient of gamma functions

2012 ◽  
pp. 395-402 ◽  
Author(s):  
Yi-Chao Chen ◽  
Toufik Mansour ◽  
Qian Zou
Keyword(s):  
Complete Monotonicity ◽  
Gamma Functions

scholarly journals COMPLETE MONOTONICITY OF A FUNCTION INVOLVING THE DIVIDED DIFFERENCE OF PSI FUNCTIONS

2013 ◽  
Vol 88 (2) ◽  
pp. 309-319 ◽  
Author(s):  
FENG QI ◽  
PIETRO CERONE ◽  
SEVER S. DRAGOMIR
Keyword(s):  
Divided Difference ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Complete Monotonicity ◽  
Divided Differences ◽  
Psi Function ◽  
Gamma Functions ◽  
Completely Monotonic ◽  
Polygamma Functions ◽  
Necessary And Sufficient

AbstractNecessary and sufficient conditions are presented for a function involving the divided difference of the psi function to be completely monotonic and for a function involving the ratio of two gamma functions to be logarithmically completely monotonic. From these, some double inequalities are derived for bounding polygamma functions, divided differences of polygamma functions, and the ratio of two gamma functions.

scholarly journals A Solution to Qi’s Conjecture on a Double Inequality for a Function Involving the Tri- and Tetra-Gamma Functions

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1098 ◽  
Author(s):  
Ladislav Matejíčka
Keyword(s):  
Open Problem ◽  
Complete Monotonicity ◽  
Double Inequality ◽  
Gamma Functions

In the paper, the author gives a solution to a conjecture on a double inequality for a function involving the tri- and tetra-gamma functions, which was first posed in Remark 6 of the paper “Complete monotonicity of a function involving the tri- and tetragamma functions” (2015) and repeated in the seventh open problem of the paper “On complete monotonicity for several classes of functions related to ratios of gamma functions” (2019).

An integral representation of the Catalan numbers

2015 ◽  
Vol 3 (3) ◽  
pp. 130 ◽  
Author(s):  
Xiao-Ting Shi ◽  
Fang-Fang Liu ◽  
Feng Qi
Keyword(s):  
Integral Representation ◽  
Open Problem ◽  
Catalan Numbers ◽  
Complete Monotonicity ◽  
Gamma Functions

<p><span>In the paper, the authors establish an integral representation of the Catalan numbers, connect the Catalan numbers with the (logarithmically) complete monotonicity, and pose an open problem on the logarithmically complete monotonicity of a function involving ratio of gamma functions.</span></p>

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